In Defense of “Pascal’s Wager” (expanded)

I have always particularly disliked Pascal’s Wager.   First, on logical grounds, since, like Anselm’s Ontological Argument, it can just as easily lead to the Great Pumpkin or the Great Penguin, as to God as conceived by Christians (of whatever stripe).  Second, on psycho-religious.   Romeo does not pitch upon Juliet by a process of totting up her good points, and subtracting her bad (suitably weighted  statistically or otherwise), comparing the result with the similar figure for the other wenches in Verona, meanwhile having his accountant double-check for accuracy, and then proceeding (with degree X of Bayesian confidence) to the balcony of the lucky winner.   Nor do such cold considerations yield any sense of the Christian feelings and beliefs about God.

The tart-tongued psychologist-philosopher William James  felt a similar aversion.  In his essay “The Will to Believe” (1896), he writes:

You probably feel that, when religious faith expresses itself thus, in the language of the gaming-table, it is put to its last trumps.  … If we were ourselves in the place of the Deity, we should probably take particular pleasure in cutting off believers of this pattern  from their infinite reward.

"Va-banque on black !"

Nevertheless, I am uncomfortably aware of having embraced something somewhat akin -- a leap of faith across a crevasse of uncertainty, borne on the wings of reason -- in subscribing to the Nicene Creed.

Credo ut intelligam

But just now, perusing the thoughtful and chatty treatise of a (non-religious) philosopher, this:

Very few people today are impressed by Pascal’s wagers.  But decision theorists have long been using the arguments he invented … Pascal’s logic is sound. The trouble is that his starting points  no longer apply for most of us.  They are no longer “live possibilities”.

-- Ian Hacking, An Introduction to Probability and Inductive Logic (2001), p. 123

Bingo!   That crack about the Great Pumpkin  misses the mark, because that portly vegetable only comes into perspective when seen from afar, from some philosopher’s distant star.   For anyone else (with the possible exception of Seneca the younger -- vide “The Pumpkinification of Claudius”), that rotund worthy is not a Live Possibility.

Our purpose here is not to argue for the intellectual respectability of adhering to the Christian faith (or to that of Islam), but to pursue the (psycho)logical point.   For, you,  respected and right-thinking reader, have almost certainly (if you are reading these words) made a similar bargain yourself:  in embracing the Religion of Science.

Not knocking science, nor denying its partly empirical character:  ever since my seventeenth year, my almost every effort has been bent in pursuit of scientific understanding.   But such is not easily to be had, even for those who majored in scientific subjects at top-flight colleges  and never slacked or looked back.   Most of what we accept, at least outside our own field of research, we largely accept on faith.  And indeed, even within that field -- QFT or String Theory, say -- there are doctrines and assumptions you just swallow  and then push forward, not really questioning these, trying to come up with something publishable that hews to the Narrative, at least until you get tenure.   "Allez en avant -- la foi vous viendra." (That celebrated epigram was actually not uttered by a prior or a bishop, but by d'Alembert, anent the mysteries of the calculus.)   To reject science sweepingly is intellectually disasterous;  but embracing it involves certain … wagers.

(For more on the subject, try this:  Veracity and Verifiability.)

Bonus:  For a relatively friendly look at Anselmian ontology, try this.
For a previously-unpublished tractate of the Saint:
http://worldofdrjustice.blogspot.com/2015/01/saint-anselms-proof-of-perfection-of.html

[Update May 2017]  Late-breaking developments on the logico-philosophical front:
http://worldofdrjustice.blogspot.com/2017/05/a-side-bet-for-pascals-wager.html

ON DEPTH AND BREADTH (überarbeitet)

            Someone (and since I forget who, it is as if the words had passed into proverb) once said: “A brilliant person is one of whom I think: I could have done such work, if only I were ten times smarter.  But in the case of a genius [here the reference was, if memory serves, to Feynman, and the epithet might actually have been not “genius” but “magician”], I can’t even imagine how it might be done.” 

            That is the depth dimension, often commented upon.

            Less obtrusively, because  by its nature  never to be noticed save over time,  is a baffling precellence of breadth.

   
  This thought arises as I finish Ian Hacking’s The Taming of Chance.  Hacking is unfailingly intelligent, but not deep beyond one’s reach.  He has a modest, easy style.  He’s not a bibliographic bully, forever quoting Kant or Toqueville or whoever you haven’t read, a propos of everything and not always with necessity (“Will the Red Sox prevail next season?  Only time, as Aquinas would have it, will tell.”).  He does not throw up a Potemkin village of supposed sources, a bibliography stuffed with Lukacs and Plato, longer and denser than the slender article it supports, topped off with epigraphs from Wallace Stevens and Valéry. Yet with everything of him I come across, he reveals a new side of him.  A polymath;  forsooth, a polytope.

            The first thing of his I read – and warmly recommend – was The Emergence of Probability. Here he seemed one of those philosophical mathematicians-manqués of the stripe of Putnam or Quine, who write with wit and erudition about technical subjects, but (one eventually finds) pretty much plow the same furrow in their various works.  Only, in later works he reveals himself as a closet Foucault fan (to this reader, as far from Kolmogorov as, I don’t know, a Red Sox fan).   And he’s written complete books on purely psychological subjects.  In The Taming of Chance, he returns to the subject of Emergence from a (crucially) slightly different angle, so that the book covers much of the same ground  but with a very different feel and specificity.   It doesn’t even have a bibliography, you have to dig it out of the footnotes.  Yet see what the spade unearths! Page after page of primary sources, like one William Turnbull’s Treatise on the Strength, Flexure, and Stiffness of Cast Iron Beams (London, 1831), or of secondary ones from obscure nooks, like the Tübinger Zeitschrift für Staatswissenschaft 4 (1863).  He cites Bernoulli, fair enough – but wait, not (or rather, not only) the celebrated Jakob of the Ars Conjectandi (which --though I haven’t read it and probably never will-- is a recognized landmark in the field),  but Johann – yet wait again, not that Johann, that familiar Johann “Jock” Bernouilli whose works you probably have on your night-table, but the later one; and not his mathematical publications neither, but rather his  no doubt in its day rightly celebrated  Reisen durch Brandenburg, Pommern, Preussen, Curland, Russland und Pohlen, published in four volumes over the course of that busy year of 1779-80 (in memory still green), and of which Hacking’s unobtrusive morsel is quarried from volume two.

            This is not what is meant by being merely, or even hugely, “well-read”.  Well-read means you’ve read all the classics throughout history in every major language in every field, and absolutely every scrap of anything at all in your own particular specialty (published or in preprint – or in papyrus --  ancient or modern), plus the odd condiment from among contemporary novels, Doonesbury,  or the folks at Port-Royal.  That’s hard enough-- I read all the time; always have; and am still just hitting the high points (and forgetting much).  Yet given 400 hours in a week instead of forty, and a couple of lifetimes tacked end to end, plus total recall, one can imagine doing it.  But the “Compte rendu des travaux de la Société phrénologique pendant le cours de l’année 1839”, which Hacking uses to such telling effect, is not on anybody’s reading list.  The ergodic reader ranging over all space  would perish in the heat death of the universe before striking upon this. 

            In fact, the whole situation puts me in mind of what Lszlew Brnzowlski so memorably said in his (partially encrypted) diary entry for 3 April 1648 (U. Tbilisi MS #9784-K) --…  No it doesn’t.  Haven’t read it.  Never heard of it.

Postscript.

            

Hacking himself can strike a stance of amazement at (allegedly) recondite knowledge.  In a chapter on philology (in Historical Ontology, p. 141), citing Foucault’s discussion of Schegel, Bopp, and Grimm, he exclaims: “Who on earth was Bopp?”  (One of the most celebrated names in the history of philology, that’s who.)  This is no doubt a pose, to let the reader catch his breath, and to chummily pretend that we’re all just struggling along here together, lads -- the way someone expounding physics for a lay audience will strive to make it all “more accessible” by sprinkling-in little apology-markers (“what physicists call the ‘spin’ of a particle known as the ‘electron’”;  “the so-called ‘Higgs boson’”;  “something called a ‘photon’”).  But shortly thereafter, Hacking himself calmly goes on to dust off such truly obscure proto-philologists as, um, “Chladenius”...

And if all that is making you feel stupid (as it certainly should),  here’s something to make you feel even stupider:

        De Stultitiâ

*

One naturally does not notice, upon first or second acquaintance, any lack of breadth  in any favorite author of your own.  You go to him for some few things, whatever they might be, and are delighted to find them again.  We do not reproach the humble hamburger, for failing to be a quail;  nor the quarterback, for lacking the qualities of a third-baseman; nor Dickens, for his obstinate indifference to the more recent developments of the higher calculus; nor indeed the Gospels, for lacking tomorrow’s weather forecast. Yet if some author comes to be our guide, our lens upon the variety of life, we do  in time  notice any astigmatism, or narrowness of the field of view.

            For some time, Orwell was my cherished author, seemingly spanning great territories: as novelist, memoirist, and critic – nay, ever as a fighter at the front --: noted in particular for his splended essay attacking insularity, “Inside the Whale”.   It was only a chance remark of his, apologizing for not having read more than several dozen of the (delightful, but) trifling novels of P.G. Wodehouse, that it struck me, how much had escaped his notice while he was so occupied:  scilicet, virtually every world-shaking intellectual development, be it in physics, mathematics, biology, philosophy,  from the mid-19^th century   on.

            Tolkien created a world, Middle Earth,  commended (in Webster’s Encyclopedia of Literature) as “one of the more detailed of all fantasy worlds”, yet which always struck me as narrow to the point of suffocation.  GKC  creates an  in some ways  similar world, but which has airholes into the infinite, which let us breathe. C.S. Lewis, in his childhood, together with his brother, created such a puppet-theatre world, reminiscences of which survive in his adult fiction; but he bursts its walls decisively  in all his essays.  His world is wider; retaining (in his own metaphor) the furniture of the nursery, side by side with the cold hard sunlight of the new world.

            It was in the course of reacquainting myself, with the saga of Greek antiquity, and Roman valor, that I happened to notice  the absence of any echo thereof, in any of the aforementioned authors. (The mindworld of Lewis embraces Northern mythology, but nothing earlier.)

*

Other such instances.

Re Otto Rank, Ernest Jones speaks of

… his truly vast erudition;  it was quite mysterious  how he found the time to read all that he did.  One of the compliments I treasure in my life  was when he asked me wherever I had found all that material in one of my non-medical essays;  that the omniscient Rank should be impressed, signified much.

-- Ernest Jones, Freud: Years of Maturity (1955), p. 160

Richard Fortey, Earth (2004), p. 314:

            One of the chief proponents of the [Snowball Earth] theory is Paul Hoffman at Harvard, one of those American academics who seem to have twice their fair share of energy. If expertise is defined as knowing  more and more  about less and less,  I am at a loss to describe what it is to know more and more  about more and more – but that is the Hoffmann condition.

*

In a work, written in English, and  ostensibly directed at engineers and physicists, subsequent to a discussion of infinitesimal deformation and path systems, we read:

We shall not go further into this approach here.  It is done quite simply and naturally in a classic paper by J. Radon.  Indeed, since this paper is one of the clearest and most elegant in the entire history of the calculus of variations, we prefer to suggest to the reader  that he consult it directly.

-- Robert Hermann, Differential Geometry and the Calculus of Variations (1968), p. 257

An admirable suggestion!  One hopes, however, that our pocket-protector-sporting anglophone engineer has been keeping up his German, and has ready access to an enormous research library, since it was published in that language (“Zum Problem von Lagrange”) back in 1928, in a relatively obscure series (Hamburg. Math. Einzelschriften, Leipzig).

*

[Update Jan 2012]  Freeman Dyson on his depth stage and his breadth stage:
http://moreintelligentlife.com/content/ideas/charles-nevin/60-year-job-freeman-dyson

~            ~            ~

For a different essay covering distinct though similar ground, try this:
http://worldofdrjustice.blogspot.com/2010/12/on-scope-and-difficulty.html

For depth itself, as deep as it gets (which is in mathematics),  this:

http://worldofdrjustice.blogspot.com/2014/01/a-dive-to-depths-expanded.html

Consilience and Cognitive Science

In a recent essay, the polymath philosopher Ian Hacking, as the first and most fundamental of his list of “applications” of mathematics, puts “App 0:  Math Applied to Math”.

Why should there be so much ultimate connectedness …?  If we follow the cognitive scientists who think that there are distinct mental modules for arithmetical reasoning and for spacial reasoning, Descartes’ Geometry of 1637 is all the more astonishing.  This question needs a lot of philosophical work, right now.

-- Ian Hacking, “Why is there Philosophy of Mathematics at All?”, repr. in Mircea Pitici, ed., The Best Writing on Mathematics 2012, p. 248

Well, here’s a tidbit towards that.

Hacking is right, that the Idols of the Neuroscientists make the success of Descartes’ breakthrough the more astonishing, as indeed they do any of the insights of mathematicians.  But that simply redounds to the discredit of the Neuroscientists.

Hacking happens to have chosen an instance of Consilience that neatly matches two pre-posited “modules” of the CogSci crowd.  (Such “modules” can be had for the asking, according to fancy;  there is no net, in that tennis-game.  -- Table-tennis, rather.  -- Right now, my “Stuff and Nonsense!” module is blinking red.)   But they would be rather more hard-pressed to come up with a separate “point-set topology module”, “abelian group theory module”, “number-theory module”, “operator theory modules”, “ring theory module”,  ET cetera ET cetera, to attempt to account all the sundry other intersubdisciplinary interilluminations which keep arising within mathematical practice -- deep connections among concepts that never fell within human ken, back when our geometry module, in collaboration with the arithmetical module, was calculating the angle and distance to the rampaging mastodon, yet which now yield such fruits as the beans Jack received in barter for a cow.

Perhaps the explanation lies well apart from the contingent biochemicalisms of the grey-matter blancmange in our brainpan, modular or otherwise.   Mayhap there is an actual unity -- a unity in variety, which we do but discover --

in bits and glimpses,

in pieces and snatches,

by dint of much study,

and by grace of Grace.

~

We are making a New Year’s Resolution, not to be so darned snarky.  (Having successfully shed nearly twenty pounds this past calendar year, we are ready to take on even greater challenges.)

Accordingly, so as to redeem our good standing among our Cognitive Scientist brethren (with whom we used to rub elbow-patches daily, back at UC Berkeley, in the permanent “temporary building” T-2), we herewith offer an extra-virgin olive branch:   preliminary results from a massive structural-neuro-longitudinal study undertaking by the Pataphysical Department of the World of Dr Justice (headquarters:  Geneva), abundantly funded by the grateful taxpayer.  With this we obtain direct insights into the child’s developing mind.   As our investigations prove, this comes pre-compartmented into the following empirically buttressed cubby-holes:

(1)  The “Everything is What it is and Not  Another Thing” foodstuff module.

The vegetables are bad enough, but when they touch the mashed potatoes -- Eeewwww.

(2)  The “Mine and Thine” module.

Though discernable in outline already in the early embryo, this module does not become activated until much later in development;  and in some specimens (B. Madoff, D. Trump) never.

Prior to activation -- much like the notocord that serves the embryo until the spinal column takes its place -- behavior is governed by the following, non-modular (“opportunist”) pragmatic maxim:

     “My bear.  My toy.  Mine.”

(3)  The “Girls Have Cooties” module.

For reasons not yet well understood, this module is activated only in immature males;  some genetic link to the Y chromosome is suspeced.  In any event, it is normally de-activated at puberty.

The Ontology of Psychology (ter)

To begin, explicit talk of structural units:

The unit of social intercourse is called a transaction.

-- Eric Berne, Games People Play (1964)

Whence the label for the analytic/therapeutic movement he launched, “Transactional Analysis”.

Birdwhistell calls each of these movements a kine, or the smallest recordable movement.

-- Julius Fast, Body Language (1970)

… the collective unconscious  and the functional units of which it is composed -- the archetypes.

-- Anthony Stevens, Jung: A Very Short Introduction (1994), p. 47

~

The notion of a culture unit, the most basic element of all, has been around for over thirty years, and has been dubbed by different authors  variously as mnemotype, idea, idene, meme, sociogene, concept, culturgen, and culture type.  The one label that has caught on the most, and for which I now vote to be winner, is meme.

Edward O. Wilson, Consilience (1998), p. 136

Actually, in anthropological and folkloristic structuralism, the notion of such units has been around rather longer than that -- Wilson cites an example himself, George Murdoch’s “classic 1945 compendium”. --   Anyhow, Wilson believes that, by working with such postulated units (how like an atom; how like a gene) we may pursue “the central program of consilience, in this instance the causal connections between semiotics and biology."

Causal, note;  strong stuff.  Even physics has in many areas backed off from this terminology of the one-way street.  (What caused the pion to decay at that precise instant, rather than another?  Um…)

~

Psychiatry, like any branch of medicine, seeks to heal.   And though  a priori  ills need not come packaged in discrete categories, it is so much more convenient if they are.

Character disorders  do not form a nosological unit.

 -- Otto Fenichel,  The Psychoanalytic Theory of Neurosis (1945), p. 539

The old pathological approach, which persists in general psychiatry to this day, describes mental illnesses  as distinct ‘entia’, each presenting a specific clinical picture.

-- Anthony Stevens, Jung: A Very Short Introduction (1994), p. 123

The taxonomy of physical nosology was aided by the discovery of pathogens,  freeing the clinician from the ambiguities of symptomatology.   Where these are absent or multiple, the disease is often ill-defined -- cf. the complexus of the various cancers.  

A historical example:

As to the nosological status of paranoia, Freud agreed with Kraepelin that it should be grouped together with the various forms of dementia praecox, rather than being a distinct entity.

-- Ernest Jones, Freud: Years of Maturity (1955), p. 271

Psychiatry gets even less guidance from microbiology or histology, leaving its taxonomic task problematic.   The attempt is made, nonetheless, every several years, to formalize this down to the last detail, in the much-discussion DSM -- the Diagnostic and Statistical Manual of mental disorders.   Aetiologically problematic to begin with, their stabs at classification have by now been largely divorced from genuine science, the DSM serving mainly simply as a tool for getting reimbursed by insurance companies, rather than any actual assistance to the diagnostician.   The whole enterprise descends to the level of a reductio, as various prickly pressure-groups veto the identification of the misbehaviors that typify them.  These, then, are meekly deleted.  (The labels vanish; the behaviors persist.) Yet the protestors have won but a Pyrrhic victory, as they still need treatment, and want to be covered by insurance;  hence the medical profession must invent euphemistic new categories to cover the old territory.

“There are no schizophrenics;

there are People with Schizophrenia.”

-- Elyn Saks,  2013;  professor of law, and herself a schizophrenic

That slogan, although posing as the denial of the existence of a certain class of entities, while affirming that of another (oddly, coextensive with the one that supposedly does not exist),  has actually nothing to do with ontology, but is simply a familiar move  in the game of rhetorical manipulation by interest groups.   Whether schizophrenia does or does not form a “nosological unit”, is a very open question;  but this “People With …” ploy  is a mere quibble.

A sort of upside-down version of that rhetorical move, from general medicine rather than psychiatry:

Even the hard-headed authors of current medical textbooks  sometimses find it necessary to inform their readers that [quoting from a 1953 text] ‘there is no disease, only the diseased … disease has no real existence.’

-- Jonathan Cohen, The Diversity of Meaning (1963), p.

 138

~

 

While we’re (sort of) on the subject -- savor this tragic disorder which The World of Doctor Justice was the first in the world to identify:  Oligophrenia mathematica.   I shall be lobbying for its inclusion in the next edition of the DSM, and expect gigantic retroactive payouts from my insurance company.

[Update 1 Aug 2013]  The current issue of the London Review of Books  has an article by Ian Hacking on the new DSM-V.  He acutely quotes Darwin saying: “All true classification  is geneological”.  For nosological taxonomy, whether physical or psychiatric, that translates to aetiological.  And, remarkably, the NIMH has suddenly taken this philosophico-methodological precept to heart, having announced, just a week before the DSM-V was released (and thus rather spoiling the launch), “that it was going to abandon the DSM because it dealt only with symptoms.”

*

For an ususual sort of psychological thriller,

try this

Murphy Calls In a Specialist

 [Kindle] [Nook]

*

[Psycho-sociological appendix]

The more intensively we analyze the “self system”, the the more apparent it becomes  that the true unit in the social process  is not the biological entity comprised of man the organism:  rather, each unit is a person-to-person context.

-- Harold Lasswell, Psychopathology and Politics (1930; 2^nd edn. 1960; re-issued 1977), p. 287

Consilience

The unity of science consists  alone  in its method, not in its material.

-- Karl Pearson

The unity of science is a pipe-dream.

-- Ian Hacking

The learnèd world  for long has yearned,  that all knowledge might be uniformly regimented beneath the broad skirts of science -- typically led by whatever was in fashion at the time.  For a while, it was Newton.  Thus,

Hume prided himself on doing for psychology  what Newton had done for physics.  He offers a (vacuous) theory of the association of ideas  as the counterpart to the theory of gravitation.

-- Anthony Kenny, The Oxford Illustrated History of Western Philosophy (1994).

In the 1920s, Otto Neurath headed up the influential Unified Science movement, which set the intellectual tone for a whole generation.

Subsequently, various technical developments have proved alluring to architects of airborne palaces -- computers in particular. As, “Hey, maybe the mind is just a Turing machine !  Tape goes to the left, goes to the right, scribble, erase,  and, bingo!,  you get Hamlet and the Credo.”  This eructation was dignified with the title of “machine-state functionalism”.

In our day, in the English-speaking world, the lodestone is Darwin.

In a lengthy work  unfortunately titled Darwin’s Dangerous Idea (1995), Daniel Dennett effectively claims skeleton-key status for Darwinism, comparing it to “universal acid:  it eats through just about every traditional concept”, including in cosmology and psychology.  A clear-headed corrective to his claims, from the ever-trenchant H. Allen Orr, may be read here: http://bostonreview.net/BR21.3/Orr.html.

~     ~     ~

And then Edward O. Wilson weighs in, with his much-talked-about book Consilience: The Unity of Knowledge (1998).   Wilson is the man to beat, when it comes to ants;  has he likewise managed to outline a Theory of Everything?   The dust jacket is certain that he has:  “nothing less than a daring challenge to the prevailing world-view ... a grand, coherent conception,  encompassing the sciences, the arts, ethics and religion” burbles Gerald Holton on the back cover, and Jared Diamond proclaims the eminent ant-man “one of the twentieth century’s greatest thinkers”.

Well, a man is not on his oath, in jacket copy.   Let us see whether the accomplishment matches the hype.

Wilson borrows the word from an 1840 work by William Whewell, which states:

The consilience of inductions takes place when an induction, obtained from one class of facts, coincides with an induction, obtained from another different class.  This consilience is a test of the truth of the theory in which it occurs.

Wilson comments: “Consilience is the key to unification.  I prefer this word over “coherence” because its rarity has preserved its precision.”  (p.8)

That is a common and valid reason for philosophical neologism (since the word consilience had become obsolete, Wilson effectively re-introduced it).  The word is not, however, used with much precision in this book -- at least, it does not truly preserve whatever meaning Whewell may have had in mind (his own wording is none too precise.)

Consilience -- It is a lovely word, rhyming with brilliance and resilience.  Wilson trots it out from time to time, rather like those “station identification” messages required by the FCC;  but over the whole course of the book, it seems to do no actual work.   As he himself suggests, it is roughly a synonym of coherence -- which would seem to be setting the bar pretty low.    

As Wiki  puts it:  “Wilson's concept is a much broader notion of consilience than that of Whewell, who was merely pointing out that generalizations invented to account for one set of phenomena often account for others as well.”  But broader is a nice way of saying diluted, weakened. --  In terms of ambition, however, Wilson’s consilience is a stronger program, in that it aims to rope in the humanities as well; but it can hope to do this only at the expense of diluting the proposed commonality.

For sheer emptiness, it touches bottom on page 117:

But surely, skeptics will say, that is impossible.  Scientific fact and art can never be translated  one into the other.  Such a response is indeed the conventional wisdom.  But I believe it is wrong.  The crucial link exists:  The common property of science and art  is the transmission of information.

Omigosh,  we didn’t we think of that before ?!?  All-kina stuffs uses information!! -- Or rather, “the information”, in the unidiomatic jargon being peddled by James Gleick’s recent (and similarly overambitious) book. -- In point of fact, there is more commonality between a sermon and a sex pheromone, since both, in addition to transmitting information, exhort. --

Or again:  We may regard elephants and chimps as simply alternate aspects of a single superorganism, since both may be seen as machines for processing peanuts into poop.
Or again, p. 219.  He quotes with approval: “Edward Rothstein, a critic trained in both mathematics and music, compares their creative processes”:

We begin with objects that look dissimilar.  We compare, find patterns, analogies with what we already know.  We distance ourselves and create abstractions…

I’d be prepared to concede (and the suggestion is intriguing) that, at a high and abstract level, there are similarities between the appreciation of … well, certain types of music (not “Who Let the Dogs Out”) and mathematics.  But surely the creative processes are quite different.   The description above (which does rather sound like a mathematician’s work)  is itself already such an abstraction, that it rings less like an analysis, than like a really terrific pick-up line  for naive and impressionable co-eds.

(There is a wonderful app, by the bye, for mathifying, or at least patternizing, our musical appreciation:

An animated graphic showing interval type

http://www.youtube.com/watch?v=X1QM6YZC45g&src_vid=asDXpfFMKNA&feature=iv&annotation_id=annotation_587547

Disney did something similar at the beginning of “Fantasia”, but this display is more precise and structured, and ultimately just as evocative as the artistic impressionism.)

However, there is another way of reading Whewell’s definition, which, whether or not Whewell himself meant it this way, leads to a more interesting notion, which we may call strong consilience.   This thesis, I shall argue, is exciting, though false; whereas the watered-down weak consilience is little more than consistency, and thus is uninteresting even if true.

[Note:   I have only just this minute stumbled upon the fact that H. Allen Orr has already written a (typically incisive) review of Consilience as well. That man is hard to top, whenever he opens his mouth about something.  So out of respect for the reader’s time, I must in all candor now urge you to cease reading this one, and go read Orr instead:

http://bostonreview.net/BR23.5/Orr.html

If, after you have savored and assimilated what Orr has to say (and which, fwiw, I heartily endorse), you still have appetite left for some leftovers, you may return to the present on-going essay.

Orr himself, incidentally, writing with Jerry Coyne, downplays consilience even within biology, in that the essential species concept is itself not tightly unified:

Because we rejected ecological differentiation as part of the Biological Species Concept in sexually reproducing groups, we obviously endorse the use of different species concepts in different groups.  We do not consider this pluralism to be a weakness of the BSC.  Because the causes of discreteness may well differ among taxa, so may the concepts appropriate to addressing the species problem.

Jerry Coyne and H. Allen Orr, Speciation  (2004), p. 52 ]

~

~  Posthumous Endorsement ~

"If I were alive today, and in the mood for a mystery,

this is what I'd be reading: "

I Don't Do Divorce Cases

Murphy on the Mount.

(I am William Whewell, and I approved this message.)

~         ~

~

(To resume...)  ]

So, let us see if we can force an interpretation on Whewell’s words which will lead to something interesting.

An “induction”, whatever exactly that may be, is not a fact, but an orderly pattern of facts.   So let us by fiat define  strong consilience thus: 

actual isomorphism (or at least homomorphism) between established aspects of different disciplines. 

The model for what we have in mind  is the collection of surprising and delightful structural coincidences within and between mathematics and various parts of (originally) mostly physics, known under the slogan of the unreasonable effectiveness of mathematics.  (You can consult Wigner’s original essay of that title here.)  And since Wigner wrote, the essence of the history of mathematics over this past half-century or more, has been an efflorescing of consilience in just this neo-Whewellian sense:  subfield after subfield  turn out to be deeply interlinked.  It is a breathtaking tale (and has, incidentally -- see below -- nothing whatever to do with the thesis of Reductionism).

There have also been some remarkable recent examples of consilience between math and physics:  cases in which mathematicians, burrowing from (as it were) the east coast, and physicists, burrowing from (so to speak) the west, suddenly met in the middle.  Celebrated cases include:  fibre bundles (math) and gauge theories (physics); zeros of the Riemann zeta-function (math) and atomic energy levels  (physics).  These results are, I suspect, among the most important of the past century (as much as to say:  of the past two millennia), and the best thing would be for us all to quit our day-jobs and join mountaintop monasteries set up specially to study these matters.  (While not omitting matins;  first things first.)

Mathematics itself might be defined as the science of matching patterns;  so there is a certain appropriateness that it serves as a link between such superficially disparate phenomena as the pattern of spots on a leopard and the subject of reaction-diffusion equations (pioneered by none other than Alan Turing), or floret patterns and Fibonacci series.  An absorbing book on this subject is Life’s other secret (bad title, good book), by Ian Stewart, 1998.

“Strong Program” publications, that go way beyond such vacuous ecumenism, include the Encyclopedia of Unified Science (Vienna Circle).

[A more careful consideration of this kind of consilience  is available here.]

 

~     ~     ~

There are times when Wilson does seem to be talking about something like strong consilience  (p. 125):

The natural sciences have constructed a webwork of causal explanation  that runs all the way from quantum physics  to the brain sciences and evolutionary biology.

Yet at other times  (p. 229), consilient seems no more than a ten-dollar synonym for consistent:

The biological origin of the arts is a working hypothesis, dependent on the reality of the epigenetic rules … It is meant to be testable, vulnerable, and consilient with the rest of biology.

Which is to say:  When attempting to demonstrate that various foul-smelling chemicals lead directly to the Goldberg Variations  and  Paradise Lost, you’re not allowed to actually falsify the basic biological facts.

~      ~      ~

Wilson never explicitly defines the characteristics of consilience once and for all -- which is fine;  it’s more a term to guide the thoughts along.   I use “minimalism” in a similar way, in these essays:  connotation accretes to the term in the course of investigation.  And a connotation that accretes to Wilson’s term  is that of hierarchy:  which has indeed characterized biology ever since Linnaeus, and in ever richer ways since, but which seems a very odd fit for, say, mathematics or art.  P. 182:

The crucial difference between the two domains is consilience:  the medical sciences have it and the social sciences do not.  Medical scientists build upon a coherent foundation of molecular and cell biology.  They pursue elements of health and illness  all the way down to the level of biophysical chemistry. … Social scientists  by and large  spurn the idea of the hierarchical ordering of knowledge…

Sidenote:

Steven Pinker (The Blank Slate,p. 26) quotes from anthropologist Leslie White  the sort of statement that apparently drove the worthy Wilson u-batz:

The culture process [is] sui generis;  culture is explainable in terms of culture.

Not, note, even in terms of psychology;  let alone physics.

Anyhow:

If being hierarchical is a requirement for being consilient, then indeed the term in this sense is more substantive than it seemed when the author proclaimed that simply using “information” would suffice.  And accordingly it becomes more falsifiable (philosophically, this is a good thing), but also (though I won’t argue the point further) in the case of many quite respectable spheres of activity, false (not so good).

~      ~      ~

Wilson’s penultimate chapter is titled “Ethics and Religion”.   Its motto (p. 238) is:

Moral reasoning, I believe, is  at every level  intrinsically consilient with the natural sciences.

Now -- those of you who have followed this blog (in particular my intemperate trashing of morally reductionist neuroscientists), no doubt expect, that at this point I shall undergo the Incredible Hulk transformation and start blasting-out one of my patented rants  against atheists (for Wilson manfully avows himself, not really an atheist, but an a-theist, a non-theist), Nominalists (Wilson is, in general, not that), and Donald Trump (so far as I know, Wilson has never even met the man).  Well, not a bit of it.

First of all, because I myself do not pretend to really understand moral reasoning.  Logic, yes, given the premises;  but ahh, the premises !  But more important, because Edward O. Wilson is a remarkably genial and congenial companion;  and one who, given his deeply Christian upbringing, truly understands what it’s all about, even if he has reached different conclusions from those of his Protestant evangelical tutors (as have I).  Furthermore, it would seem that both the present and the previous Pope would agree with that statement.

He clarifies:

The split is not, as popularly supposed, between religious believers and secularists.  It is between transcendentalists [dbj:  cf. Realists], those who think that moral guidelines exist outside the human mind,  and empiricists [dbj: cf. Nominalists], who think them contrivances of the mind.  The choice between religious or nonreligious conviction  and the choice between ethically transcendentalist or empiricst conviction  are cross-cutting decisions made in metaphysical thought.

Absolutely true.  There is, of course, a question about how non-theistic and indeed non-deistic transcendental moral schemes are grounded, but that does not invalidate the logical point made here.

As Charles C. Gillispie puts it in his generous review:

Put baldly, this sounds like arid monistic materialism. Wilson does not put it baldly. He brings to his subject a disarming mixture of personal modesty and intellectual rigor. His reading is wide and his learning extensive. He writes as well of arts and letters as he does of science. It is difficult to think of a finer evocation of Milton's genius than Wilson’s passage on Satan’s invasion of the garden of Eden.

(Um, well, actually, not so much:  C.S. Lewis, A Preface to Paradise Lost.  Still, Wilson’s own tribute is very creditable indeed, for a myrmecologist.)

He adds:

There is no question in his mind but that conveying the essence of truth and beauty pertains to the arts.

You (as Sarah Palin would put it) betcha !  But -- contrary to the effusions of certain journalistic science-pornographers, “conveying the essence of beauty” is not, in fact, the brief of science.

~      ~      ~

The latter part of the book contains rather general sociopolitical discussions:  which, at his own assessment that the social sciences are lamentably unconsilient, means that we stray fairly far from genuinely scientific or Whewellian concerns. 

Despite the fact that his overarching project is ambitious (or made to sound so), Wilson himself is a becomingly modest man.  He even cops to a probably spurious potential charge, granting a “whiff of brimstone in the consilient world view, and a seeming touch of Faust to those committed to its humanistic core.”  Specifically, he points to the spectre of human genetic engineering:  “How much should people be allowed to mutate themselves and their desendants?”  The spectre is quite real, the charge being spurious only if laid at the door of a Whewellian philosophy of science.   What eventually -- or not-so-eventually -- comes to pass, will depend, neither on philosophy nor on theoretical science, but on what is fashionable and funded in places like Singapore and Hong Kong.  It is quite possible that, within the lifetime of some of you, you will witness a Wellsian world of Eloi and Morlocks.   Institutionally, not much stands in the way of this but the Historical Church.

~     ~      ~     ~     ~

This may be a tad off-topic but... The Atlantic Monthly has just published a very nice article on Professor Wilson's current activities.  Of particular interest to myself was reference to an article that Wilson recently co-authored with Martin Nowak, a splendid mathematical biologist whose acquaintance I had the pleasure of making at a conference he organized at the Princeton IAS, described in "Follia Linguistica" (in: Princeton Follies;  to appear).

~      ~      ~

Russell Standish, a mathematician, cites the work of his chatmate, one Bruno:

His conclusion is, instead of psychology being reducible to, or indeed emerging from the laws of physics, the fundamental laws of physics are in fact a conseuence of the properties of machine psychology.  This is indeed a revolutionary reversal of the traditional ontology of these subjects.

Russell Standish, Theory of Nothing (2006; 2^nd edn. 2011), p. 129

Such a view is certainly consilient, though it stands Wilsonian consilience on its head, along with common sense.  And Standish embraces it thus (solecistically):  “I agree with this fundamental tenant.”  By that he means tenet;  but “machine psychology” is no typo -- sic, as it stands -- albeit it would make about as much sense to derive the laws of physics rather from marine psychology :  We are all but the dreams of porpoises …

[Update 16 III 2012] A striven-for consilience of art criticism and neuroscience:
http://chronicle.com/article/Eric-Kandels-Visions/131095/

Notes towards an eventual essay on Causality

The word “cause”    is an altar

to an unknown god

-- Wm. James

 

[Over the years, I have built up a file of many hundreds of pages, consisting of juicy quotes on various topics, raw materials for many a book and essay.  However, the publishing landscape being what it is, these have long lain fallow.  In all likelihood, the Reaper will be requiring an audience before all this grist can be milled.   A shame for it all simply to lie there, where the worm doth bore and the mice do gnaw.  So herewith a tiny sampling, as hostages to fortune, and a goad to the Muse.]

Let’s start things off with a quotation that sets matters in the perspective of a mystery.

Abraham Pais, a physicist and friend of Einstein, on the very first page of his technically-dense biography of Einstein (Subtle is the Lord), mentions a poser that motivated him to write the book:

I wondered once again about the question, Why does this man, who contributed so incomparably much to the creation of modern physics, remain so attached to the nineteenth-century view of causality.

We shan’t answer this here, but for now we'll merely offer a bouquet of quotes illustrating thoughts about causality, down the ages.

(1) Causality in general

Chaucer, Tale of Melibeus (following Aristotle):
"The wrong that thou hast received  hath certain causes, which that clerks clepen Oriens and Efficiens, and Causa longinqua and Causa propinqua; this is to seyn, the fer cause and the ny cause.  The fer cause is almighty God, that is cause of all things.  The neer cause is thy three enemies.  The cause accidental was hate.  The cause material been the five wounds of thy daughter. The cause formal is the manner of their working, that broughten ladders for to slay thy daughter …"

David Hume, An Enquiry Concerning Human Understanding (1748), p.75: "He could not pronounce that the one event was connected: but only that it was conjoined with the other."   (cf., later, “synchronicity”)

David Hume, An Enquiry Concerning Human Understanding (1748, 1777), p. 76:
"We may define a cause to be an object, followed by another, and where all the objects similar to the first  are followed by objects similar to the second.  Or in other words where, if the first object had not been, the second never had existed." 

These are not in fact equivalent formulations.  The first is too broad, and would apply to prefaces and books.  The second would not apply to these, as there exist books without prefaces.

Hermann Paul, Prinzipien der Sprachgeschichte (1880, 5^th edn. 1920), p. 24: "Denn zwischen Abstraktionen gibt es überhaupt keinen Kausalnexus, sondern nur zwischen realen Objekten und Tatsachen."

Ward & Waller, eds. The Cambridge History of English Literature, vol. I:  From the Beginnings to the Cycles of Romance (1907), emphasizing intralingual change rather than French influence:

The differences between the grammar of Old English  and that of the English of Chaucer’s day must be ascribed to internal agencies.

"The law of causality, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm."
Bertrand Russell, "On the Notion of Cause" (1912).

P.A.M. Dirac, The Principles of Quantum Mechanics (1930; 4^th edn. 1958), p. 4:

We must revise our ideas of causality.  Causality applies only to a system which is left undisturbed.  If a system is small, we cannot observe it  without producing a serious disturbance  and hence we cannot expect to find any causal connexion between the results of our observations.  Causality will still be assumed to apply to undisturbed systems.

Robert Lindsay & Henry Margenau, Foundations of Physics (1936), p. 522:

That many miracles have allegedly been predicted, is hardly sufficient to reconcile their occurrence with the causality postulate.  We conclude:  The positivistic formulation, with its main emphasis upon human ability to know, does not express the nucleus of what is understood by causality.

As to what does express this nucleus (they go on), it is somewhat surprising to the average man on the omnibus:

Consistency of nature, i.e. causality, may be characterized by saying: The differential equations  in terms of which nature is described,  do not contain explicit functions of the time.

This is followed by more technical observations concerning “impressed forces”, and closed vs. open systems.

Mark Sullivan, Our Times VI (1939), p. 74: "I doubt whether a nomination for the Presidency (or anything else) ever merely 'happens', always it must be brought about  and always somebody must play the part of bringer-about."

A. D’Abro, The Rise of the New Physics (1939), vol. II, p. 944:

When Planck advanced his quantum theory of equilibrium radiation, science was confronted with a doctrine in which the succession of events  was not continuous, and in which  causal relations between successive events  were not specifically asserted.  The highly speculative nature of Planck’s ideas  prevented them from receiving immediate acceptance;  but around the year 1907, the remarkable successes of Planck’s theory in other realms of physics  silenced all opposition, and from then on  serious doubts were cast on the validity of rigorous causality in physical science.

Nonlinearity entails noncausality … Causality is a first approximation … a linear approximation to determinism.

Mario Bunge, Causality and Modern Science (1959, 1963).  He traces the ancestry of this insight to Bridgeman, The Logic of Modern Physics (1927).

A.J. Ayer, Scientific American, Oct 1965: "Even in a field in which causal laws are well established, there is often a certain looseness in the way they fit the facts. … These slight deviations are not held to be significant; they are ascribed to errors of observation.
            'Errors of observation', however, is here a term of art.  Apart from the existence of the deviations, there is usually no reason to suppose that any errors have occurred.  Now, I think it possible that this looseness of the fit  cannot be wholely eliminated; in other words, that there are limits to the precision with which the course of nature can be prospectively charted." This margin then is "in the hands of chance."

Resnick & Halliday, Physics (1966), p. 87:
"If one of the two forces involved in the interaction between two bodies is called an 'action' force, the other is called the 'reaction' force.  Either force may be considered the 'action' and the other the 'reaction'.  Cause and effect is not implied here, but a mutual simultaneous interaction is implied."

Nicholas Georgescu-Roegen,  The Entropy Law and the Economic Process (1971), p. 171:

John von Neumann even argued [in Mathematical Foundations of Quantum Mechanics (1955)] that this cause-effect link “has certainly no other cause than the ‘law of large numbers’”, the justification being that “the apparent causal order of the world in the large … is completely independent of whether the natural laws governing the elementary processes are causal or not.”

Nicholas Georgescu-Roegen,  The Entropy Law and the Economic Process (1971), p. 175f:

The point shines in Planck’s statement  that the principle of causality “is neither correct nor incorrect;  it is a heuristic principle; … it is the most valuable pointer that we possess … to find a path through the confusion of events.  … [Yet] Planck, after recognizing that causality is only a heuristic principle, let his inner convictions  sweep him away, and, without any ado, proclaimed that causality is “an almighty law  which governs the world”.

Without attempting to proselytize, let us merely here mention the Christian view that, indeed, an almighty law does govern the world, but that the relative ‘causal’ and ‘a-causal’ portions  remain to be determined. -- And notice the scheme of C.S. Lewis, whereby the Natural is wholly given over to the causal, whereas the a-causal (in the Newtonian/Laplacian sense) is confined to the Supernatural and… the Subnatural (the quantum).

Peter Geach, in Reason and Argument (1976, p. 3), urges "a threefold distinction: motives for belief, reasons for belief, causes of belief."

Mario Bunge, preface (1979) to third edition of Causality and Modern Science (1959; 1963):
Positivism had always denounced causality as a myth. … Causalism, the view that all relations among events except the purely spatio-temporal are causal, is surely untenable.

Ralph Grishman, Computational Linguistics (1986), p. 92: "the usual use of 'if A then B', which conveys some causal connections between A and B – so-called strict implication rather than material implication."

Gerd Gigerenzer et al, The Empire of Chance (1989), p. 71: "Such variation could mask the effects of the agencies under investigation." (agency = causal factor)

Gigerenzer et al, The Empire of Chance (1989), p.84: "To be a cause  generally means to make a difference."

Ian Hacking, The Taming of Chance (1990), p. 123:
“The element in phrenological theory that mattered to statisticians  was that it created an argument to separate a penchant  from a determining factor.  The old slogan of Leibniz, ‘inclines without necessitating’, was given new application.”

Ian Hacking, The Taming of Chance (1990), p. 130:
“Engel had argued: we have statistical regularity, but not law, hence no causes acting on individuals to determine suicides.”

Dagegen Wagner:

“Statistical homogeneity … can result only from causation.  No law can apply to an ensemble   unless there is a set of (deterministic) laws applying to the individuals.”

Ian Hacking, The Taming of Chance (1990), p. 188:
“Pearson … testified to the correlation between the taming of chance  and the elimination of ordinary causality.”

17 XI 01 NYTimes: "Since Sept. 11, few phrases have become as familiar as "root causes." Forthright condemnations of the attacks have often been accompanied by assertions that, ultimately, the "root causes" of terror must also be addressed."

Steven Pinker,  The Blank Slate (2002), p. 32:

Behavior appears to have a different kind of trigger than other physical events.  Ordinary events have causes, but human behavior has reasons.

[continued here]